Abstract
In this paper, we study class A composition operators Cφ on the Hardy space H2. We show that if Cφ belongs to class A, then 0 is a fixed point of the symbol φ. As a corollary, we obtain that every invertible class A composition operator is unitary. Moreover, we examine spectral properties and the commutants of class A composition operators. We also prove that if φ is a linear fractional self-map of D into itself, then Cφ belongs to class A if and only if it is subnormal. Finally, we provide some conditions under which Cφ⁎ belongs to class A.
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